scipy.signal.tf2ss#

scipy.signal.tf2ss(num, den)[source]#

Transfer function to state-space representation.

Parameters

num, denarray_like: Sequences representing the coefficients of the numerator and denominator polynomials, in order of descending degree. The denominator needs to be at least as long as the numerator.

Returns

A, B, C, Dndarray: State space representation of the system, in controller canonical form.

Examples

Convert the transfer function:

\[H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}\]

>>> num = [1, 3, 3]
>>> den = [1, 2, 1]

to the state-space representation:

\[ \begin{align}\begin{aligned}\begin{split}\dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\\end{split}\\\textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)\end{aligned}\end{align} \]

>>> from scipy.signal import tf2ss
>>> A, B, C, D = tf2ss(num, den)
>>> A
array([[-2., -1.],
       [ 1.,  0.]])
>>> B
array([[ 1.],
       [ 0.]])
>>> C
array([[ 1.,  2.]])
>>> D
array([[ 1.]])

scipy.signal.tf2sos

scipy.signal.zpk2tf